Which problems in AI are not machine learning?
This is a common question and it has already been answered in many different places:

What is the difference between artificial intelligence and machine learning?


Artificial Intelligence vs. Machine Learning vs. Deep Learning


  Artificial intelligence is a broader concept than machine learning, which addresses the use of computers to mimic the cognitive functions of humans. When machines carry out tasks based on algorithms in an "intelligent" manner, that is AI. Machine learning is a subset of AI and focuses on the ability of machines to receive a set of data and learn for themselves, changing algorithms as they learn more about the information they are processing.


More specific to your question:

AI without machine learning


  If you insert a small amount of knowledge into a machine, you can call it an engineering product. But if you instill a sufficiently large amount of knowledge such that the machine makes better decisions than a human, that can be could AI. For example, if you take hundreds of medical doctors and each spends hundreds of hours detailing correlations between symptoms and disease, if you then pack that knowledge into an easy-to-use machine, that's AI without machine-learning